The doctrine of chances: or, a method of calculating the probability of events in play / By A. De Moivre.

  • Abraham de Moivre
Date:
1718
Catalogue details

Licence: Public Domain Mark

Credit: The doctrine of chances: or, a method of calculating the probability of events in play / By A. De Moivre. Source: Wellcome Collection.

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    6-]-x x iio-|- -f- xif-'x 384 + 4. x x x 431. + -f x p-1 x ip X ip x 162, or <> + 3I-j-* + 50+xjt + 3i^-,xi + or * ^ -J— X X + I X X + 2 X 3 X 4* I X 3 X + 4. ^ In like manner it will be found, that the fum of all the Terms which belong to B, the laft of which is ^X4X} is ~P“ * X+I X X+2 X 3x4-5* X 3x4-8. And alfo that the fum of all the Terms belonging to C, the laft of which is 4X3X2, is x *4-i x *4-2 x 9XX4-27X4-16. Now x in each cafe reprefents the number of Terms want- ing one, which belong feverally to A, B, C; wherefore ma¬ king jc+i = />, their feveral Expectations will be refpeCtive— ly proportional to p X 7+i X 3^2 X 3/>+i P x />+i x 3/>+2 x_3^+5* P x X 9pp~\m9p~~m'^* Again, the number of all the Terms which belong to them all being 97, and A being to take firft, it follows, that p in the firft cafe is = 33, in the other two = 32. Therefore the feveral Expectations of A, B, C will be re- fpeCtively proportional to 41225*, 39592,, 38008. If the number of all the Counters were 500, and the num¬ ber of the White ones ftill 4; then the number of all the Terms reprefenting the Expectations of Ay B, C would be 497,.. Now this number being divided by 3, the Quotient is i6y, and the Remainder 2: From whence it follows, that the laft Term 3X2X1 will belong to B, the laft but one 4X3X2 to A, and the laft but two to C; it follows alfo, that for B7 and A, p muft be interpreted by 166, but for C by 165. The
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